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We study several realistic configurations allowing to realize an acoustic horizon in the flow of a one dimensional Bose-Einstein condensate. In each case we give an analytical description of the flow pattern, of the spectrum of Hawking radiation and of the associated quantum fluctuations. Our calculations confirm that the non local correlations of the density fluctuations previously studied in a simplified model provide a clear signature of Hawking radiation also in realistic configurations. In addition we explain by direct computation how this non local signal relates to short range modifications of the density correlations.

Propagation of light pulses through negative group velocity media is known to give rise to a number of paradoxical situations that seem to violate causality. The solution of these paradoxes has triggered the investigation of a number of interesting and unexpected features of light propagation. Here we report a combined theoretical and experimental study of the ring-down oscillations in optical cavities filled with a medium with such a strongly negative frequency dispersion to give a negative round-trip group delay time. We theoretically anticipate that causality imposes the existence of additional resonance peaks in the cavity transmission, resulting in a non-exponential decay of the cavity field and in a breakdown of the cavity decay rate concept. Our predictions are validated by simulations and by an experiment using a room-temperature gas of metastable helium atoms in the detuned electromagnetically induced transparency regime as the cavity medium.

We report a theoretical study of the optical properties of a three-level emitter embedded in an optical cavity including the non-rotating wave terms of the light-matter interaction Hamiltonian. Rabi oscillations induced by a continuous wave drive laser are responsible for a periodic time-modulation of the effective cavity resonance, which results in a significant dynamical Casimir emission. A clear signature of the back-action effect of the dynamical Casimir emission onto the drive laser is visible as a sizable suppression of its absorption.

We propose and characterize solid-state photonic structures where light experiences an artificial gauge field. A suitable coupling of the propagation and polarization degrees of freedom introduces a geometrical phase for photons tunneling between adjacent sites of a coupled cavity array. We then discuss the feasibility of observing strong gauge field effects in the optical spectra of realistic systems, including the Hofstadter butterfly spectrum.

While photons in vacuum are massless particles that do not interact with each other, significant photon-photon interactions appear in suitable nonlinear media, leading to novel hydrodynamic behaviors typical of quantum fluids. Here we show the formation of vortex-antivortex pairs in a Bose-Einstein condensate of exciton-polaritons -a coherent gas of strongly dressed photons- flowing at supersonic speed against an artificial potential barrier created and controlled by a light beam in a planar semiconductor microcavity. The observed hydrodynamical phenomenology is in agreement with original theoretical predictions based on the Gross-Pitaevskii equation, recently generalized to the polariton context. However, in contrast to this theoretical work, we show how the initial position and the subsequent trajectory of the vortices crucially depend on the strength and size of the artificial barrier. Additionally, we demonstrate how a suitably tailored optical beam can be used to permanently trap and store the vortices that are hydrodynamically created in the wake of a natural defect. These observations are borne out by time-dependent theoretical simulations.

A quantum fluid passing an obstacle behaves differently from a classical one. When the flow is slow enough, the quantum gas enters a superfluid regime and neither whirlpools nor waves form around the obstacle. For higher flow velocities, it has been predicted that the perturbation induced by the defect gives rise to the turbulent emission of quantised vortices and to the nucleation of solitons. Using an interacting Bose gas of exciton-polaritons in a semiconductor microcavity, we report the transition from superfluidity to the hydrodynamic formation of oblique dark solitons and vortex streets in the wake of a potential barrier. The direct observation of these topological excitations provides key information on the mechanisms of superflow and shows the potential of polariton condensates for quantum turbulence studies., Comment: Published version with corrected colorbar scale for Fig. 3. Raw data available as ancillary files

Hawking's prediction of thermal radiation by black holes has been shown by Unruh to be expected also in condensed matter systems. We show here that in a black hole-like configuration realised in a BEC this particle creation does indeed take place and can be unambiguously identified via a characteristic pattern in the density-density correlations. This opens the concrete possibility of the experimental verification of this effect., Comment: 13 pages, 2 figures. Honorable mention in the 2010 GRF Essay Competition

We apply the microscopic Bogoliubov theory of dilute Bose-Einstein condensates to analyze quantum and thermal fluctuations in a flowing atomic condensate in the presence of a sonic horizon. For the simplest case of a step-like horizon, closed-form analytical expressions are found for the spectral distribution of the analog Hawking radiation and for the density correlation function. The peculiar long-distance density correlations that appear as a consequence of the Hawking emission features turns out to be reinforced by a finite initial temperature of the condensate. The analytical results are in good quantitative agreement with first principle numerical calculations., Comment: 11 pages, 7 figures

Resonant laser scattering along with photon correlation measurements have established the atom-like character of quantum dots. Here, we present measurements which challenge this identification for a wide range of experimental parameters: the absorption lineshapes that we measure at magnetic fields exceeding 1 Tesla indicate that the nuclear spins polarize by an amount that ensures locking of the quantum dot resonances to the incident laser frequency. In contrast to earlier experiments, this nuclear spin polarization is bi-directional, allowing the electron+nuclear spin system to track the changes in laser frequency dynamically on both sides of the quantum dot resonance. Our measurements reveal that the confluence of the laser excitation and nuclear spin polarization suppresses the fluctuations in the resonant absorption signal. A master equation analysis shows narrowing of the nuclear Overhauser field variance, pointing to potential applications in quantum information processing.

We analyze the non-equilibrium dynamics of a gas of interacting photons in an array of coupled dissipative nonlinear cavities driven by a pulsed external coherent field. Using a mean-field approach, we show that the system exhibits a phase transition from a Mott-insulator-like to a superfluid regime. For a given single-photon nonlinearity, the critical value of the photon tunneling rate at which the phase transition occurs increases with the increasing photon loss rate. We checked the robustness of the transition by showing its insensitivity to the initial state prepared by the the pulsed excitation. We find that the second-order coherence of cavity emission can be used to determine the phase diagram of an optical many-body system without the need for thermalization., Comment: 4 pages, 4 figures

One of the most striking manifestations of quantum coherence in interacting boson systems is superfluidity. Exciton-polaritons in semiconductor microcavities are two-dimensional composite bosons predicted to behave as particular quantum fluids. We report the observation of superfluid motion of polaritons created by a laser in a semiconductor microcavity. Superfluidity is investigated in terms of the Landau criterion and manifests itself as the suppression of scattering from defects when the flow velocity is slower than the speed of sound in the fluid. On the other hand, a Cerenkov-like wake pattern is clearly observed when the flow velocity exceeds the speed of sound. The experimental findings are in excellent quantitative agreement with the predictions based on a generalized Gross-Pitaevskii theory, showing that polaritons in microcavities constitute a very rich system for exploring the physics of non-equilibrium quantum fluids., Comment: 14 pages, 3 figures

The excitation spectrum around the pump-only stationary state of a polariton optical parametric oscillator (OPO) in semiconductor microcavities is investigated by time-resolved photoluminescence. The response to a weak pulsed perturbation in the vicinity of the idler mode is directly related to the lifetime of the elementary excitations. A dramatic increase of the lifetime is observed for a pump intensity approaching and exceeding the OPO threshold. The observations can be explained in terms of a critical slowing down of the dynamics upon approaching the threshold and the following onset of the soft Goldstone mode.

One of the most striking quantum effects in a low temperature interacting Bose gas is superfluidity. First observed in liquid 4He, this phenomenon has been intensively studied in a variety of systems for its amazing features such as the persistence of superflows and the quantization of the angular momentum of vortices. The achievement of Bose-Einstein condensation (BEC) in dilute atomic gases provided an exceptional opportunity to observe and study superfluidity in an extremely clean and controlled environment. In the solid state, Bose-Einstein condensation of exciton polaritons has now been reported several times. Polaritons are strongly interacting light-matter quasi-particles, naturally occurring in semiconductor microcavities in the strong coupling regime and constitute a very interesting example of composite bosons. Even though pioneering experiments have recently addressed the propagation of a fluid of coherent polaritons, still no conclusive evidence is yet available of its superfluid nature. In the present Letter, we report the observation of spontaneous formation of pinned quantised vortices in the Bose-condensed phase of a polariton fluid by means of phase and amplitude imaging. Theoretical insight into the possible origin of such vortices is presented in terms of a generalised Gross-Pitaevskii equation. The implications of our observations concerning the superfluid nature of the non-equilibrium polariton fluid are finally discussed., Comment: 14 pages, 4 figures

We investigate the physics of coherent polaritons in a double-well configuration under a resonant pumping. For a continuous wave pump, bistability and self-pulsing regimes are identified as a function of the pump energy and intensity. The response to an additional probe pulse is characterized in the different cases and related to the Bogoliubov modes around the stationary state. Under a pulsed pump, a crossover from Josephson-like oscillations to self-trapping is predicted for increasing pump intensity. The accurateness of the effective two-mode model is assessed by comparing its predictions to a full solution of the non-equilibrium Gross-Pitaevskii equation.

We present a generic model for the description of non-equilibrium Bose-Einstein condensates, suited for the modelling of non-resonantly pumped polariton condensates in a semiconductor microcavity. The excitation spectrum and scattering of the non-equilibrium condensate with a defect are discussed., Comment: 4 pages, 2 figures

We develop a mean-field theory of the spatial profile and the spectral properties of polariton condensates in nonresonantly pumped semiconductor microcavities in the strong coupling regime. Predictions are obtained for both the continuous-wave and the pulsed excitation regimes and the specific signatures of the non-equilibrium character of the condensation process are pointed out. A striking sensitivity of the condensate shape on the optical pump spot size is demonstrated by analytical and numerical calculations, in good quantitative agreement with recent experimental observations., Comment: 5 pages, 3 figures

We have developed a mean-field model to describe the dynamics of a non-equilibrium Bose-Einstein condensate of exciton-polaritons in a semiconductor microcavity. The spectrum of elementary excitations around the stationary state is analytically studied in different geometries. A diffusive behaviour of the Goldstone mode is found in the spatially homogeneous case and new features are predicted for the Josephson effect in a two-well geometry., Comment: 5 pages, 2 figures

We study the density modulation that appears in a Bose-Einstein condensate flowing with supersonic velocity against an obstacle. The experimental density profiles observed at JILA are reproduced by a numerical integration of the Gross-Pitaevskii equation and then interpreted in terms of Cerenkov emission of Bogoliubov excitations by the defect. The phonon and the single-particle regions of the Bogoliubov spectrum are respectively responsible for a conical wavefront and a fan-shaped series of precursors.

The threshold of triply resonant optical parametric oscillation in a semiconductor microcavity in the strong coupling regime is investigated. Because of the third-order nature of the excitonic nonlinearity, a variety of different behaviours is observed thanks to the interplay of parametric oscillation and optical bistability effects. The behaviour of the signal amplitude and of the quantum fluctuations in approaching the threshold has been characterized as a function of the pump, signal and idler frequencies., Comment: 13 pages, 9 figures

We propose a general procedure for reducing the three-dimensional Schrodinger equation for atoms moving along a strongly confining atomic waveguide to an effective one-dimensional equation. This procedure is applied to the case of a rotating closed-loop waveguide. The possibility of including mean-field atomic interactions is presented. Application of the general theory to characterize a new concept of atomic waveguide based on optical tweezers is finally discussed.

The polarization produced by the relative displacement of the potentials trapping two spin species of a dilute Fermi gas with $N_\ua=N_\da$ is calculated at unitarity by assuming phase separation between the superfluid and a spin polarized phase at zero temperature. Due to the energy cost associated with pair breaking, the dipole magnetic polarizability vanishes in the linear limit and exhibits important deviations from the ideal gas behaviour even for displacements of the order of the size of the atomic cloud. The magnetic behaviour in the presence of different trapping frequencies for the two spin species is also discussed.

The pair correlation function of an expanding gas is investigated with an emphasis on the BEC-BCS crossover of a superfluid Fermi gas at zero temperature. At unitarity quantum Monte Carlo simulations reveal the occurrence of a sizable bunching effect due to interactions in the spin up-down channel which, at short distances, is larger than that exhibited by thermal bosons in the Hanbury-Brown and Twiss effect. We propose a local equilibrium ansatz for the pair correlation function which we predict will remain isotropic during the expansion even if the trapping potential is anisotropic, contrary to what happens for non-interacting gases. This behavior is understood to be a consequence of the violation of scaling of the pair correlation function due to interactions., Comment: 4 pages, 1 figure

We analytically investigate the spatial coherence properties of the signal emission from one-dimensional optical parametric oscillators. Because of the reduced dimensionality, quantum fluctuations are able to destroy the long-range phase coherence even far above threshold. The spatial decay of coherence is exponential and, for realistic parameters of semiconductor photonic wires in the strong exciton-photon coupling regime, it is predicted to occur on an experimentally accessible length scale., Comment: 6 pages, 3 figures

We theoretically study the effect of ultraslow group velocities on the emission of Vavilov-Cherenkov radiation in a coherently driven medium. We show that in this case the aperture of the group cone on which the intensity of the radiation peaks is much smaller than that of the usual wave cone associated with the Cherenkov coherence condition. We show that such a singular behaviour may be observed in a coherently driven ultracold atomic gas., Comment: 4 pages, 4 figures

We present a numerically tractable method to solve exactly the evolution of a N boson system with binary interactions. The density operator of the system rho is obtained as the stochastic average of particular operators |Psi_1> are either Fock states |N:phi_{1,2}> or coherent states |coh:phi_{1,2}> with each particle in the state phi_{1,2}. We determine the conditions on the evolution of phi_{1,2} -which involves a stochastic element- under which we recover the exact evolution of rho. We discuss various possible implementations of these conditions. The well known positive P-representation arises as a particular case of the coherent state ansatz. We treat numerically two examples: a two-mode system and a one-dimensional harmonically confined gas. These examples, together with an analytical estimate of the noise, show that the Fock state ansatz is the most promising one in terms of precision and stability of the numerical solution., Comment: 21 pages, 5 figures, submitted to Phys.Rev. A

We present a theoretical analysis of the evaporative cooling of an atomic beam propagating in a magnetic guide. Cooling is provided by transverse evaporation. The atomic dynamics inside the guide is analyzed by solving the Boltzmann equation with two different approaches: an approximate analytical ansatz and a Monte-Carlo simulation. Within their domain of validity, these two methods are found to be in very good agreement with each other. They allow us to determine how the phase-space density and the flux of the beam vary along its direction of propagation. We find a significant increase for the phase-space density along the guide for realistic experimental parameters. By extrapolation, we estimate the length of the beam needed to reach quantum degeneracy., Comment: 13 pages, 7 figures, to be published in EPJ D, revised version